Question

(a) Transform the expression (x − a)^2 + y^2 = a^2 into polar coordinates.
(b) Sketch the region R bounded by the curve given in part (a).
(c) Use a double integral in polar coordinates to find the area of the region R.

Answer 1

You know it's a circle of radius a with center at (a,0)

x^2+y^2-2ax+a^2 = a^2
r^2 = 2arcosθ
r = 2a cosθ

Integrate, but realize that the circle is traced twice as θ goes from 0 to 2π. I hope you come up with πa^2 as the area!